Systems and methods for unifying statistical models for different data modalities

ABSTRACT

Techniques for performing a prediction task using a multi-modal statistical model configured to receive input data from multiple modalities including input data from a first modality and input data from a second modality different from the first modality. The techniques include:obtaining information specifying the multi-modal statistical model including values of parameters of each of multiple components of the multi-modal statistical model, the multiple components including first and second encoders for processing input data for the first and second modalities, respectively, first and second modality embeddings, a joint-modality representation, and a predictor;obtaining first input data for the first data modality; providing the first input data to the first encoder to generate a first feature vector; identifying a second feature vector using the joint-modality representation, the first modality embedding and the first feature vector; and generating a prediction for the prediction task using the predictor and the second feature vector.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a Continuation and claims the benefit under 35U.S.C. § 120 of U.S. application Ser. No. 17/195,311, filed Mar. 8,2021, entitled “Systems and Methods for Unifying Statistical Models forDifferent Data Modalities”, which is a Continuation and claims thebenefit under 35 U.S.C. § 120 of U.S. application Ser. No. 16/406,348,filed May 8, 2019, and titled “Systems and Methods for UnifyingStatistical Models for Different Data Modalities”. Application Ser. No.16/406,348 claims priority under 35 U.S.C. § 119(e) to U.S. ProvisionalPatent Application No. 62/671,068, filed May 14, 2018, and titled“Systems and Methods for Multi-Modal Prediction”, and U.S. ProvisionalPatent Application No. 62/678,074, filed May 30, 2018, and titled“Systems and Methods for Unifying Statistical Models for Different DataModalities”, each of which is incorporated by reference in its entirety.

BACKGROUND

Machine learning technology is often applied to problems where data frommultiple modalities is available. Data may be collected using differentacquisition frameworks, each of which may be characterized by respectivedata sources, data types, data gathering techniques, sensors, and/orenvironments. Data being associated with one modality may be gathered byusing an acquisition framework that is different from the acquisitionframework used to gather data associated with a different modality. Forexample, data gathered by one type of sensor or experimental techniquehas a different modality from the data gathered by another type ofsensor or experimental technique. As another example, data of one type(e.g., image data) is not of the same modality as data of another type(e.g., text data).

There are many conventional statistical models for processing data for aparticular modality. For example, convolutional neural networks may beapplied to images to solve the problem of identifying objects shown inthe images. As another example, recurrent neural networks may be appliedto speech data for speech recognition.

It is more challenging, however, to train and use statistical machinelearning models that can effectively utilize data from multipledifferent data modalities. Such multi-modal statistical machine learningmodels would have wide applicability in a range of fields includingmedicine and biology, where there is a large number of heterogeneousdata sources (e.g., DNA, RNA and protein expression data for a patient,medical images of the patient in one or more modalities, a patient'smedical history, information concerning a disease that the patient mayhave, etc.) that could be brought to bear on a problem of interest(e.g., predicting whether a patient will respond to a particular drugtreatment).

SUMMARY

Some embodiments include a method for training a multi-modal statisticalmodel configured to receive input data from multiple modalitiesincluding input data from a first modality and input data from a secondmodality different from the first modality. The method comprises:accessing unlabeled training data including unlabeled training data forthe first modality and unlabeled training data for the second modality;accessing labeled training data including labeled training data for thefirst modality and labeled training data for the second modality;training the multi-modal statistical model in two stages, themulti-modal statistical model comprising multiple components includingfirst and second encoders for processing input data for the first andsecond modalities, respectively, first and second modality embeddings, ajoint-modality representation, and a predictor, the training comprising:performing a first training stage at least in part by estimating valuesfor parameters of the first and second modality embeddings, and thejoint-modality representation using a self-supervised learning techniqueand the unlabeled training data; performing a second training stage atleast in part by estimating values for parameters of the predictor usinga supervised learning technique and the labeled training data; andstoring information specifying the multi-modal statistical model atleast in part by storing the estimated values for parameters of themultiple components of the multi-modal statistical model.

Some embodiments include a system comprising: at least one computerhardware processor; and at least one non-transitory computer-readablestorage medium storing processor-executable instructions that, whenexecuted by the at least one computer hardware processor, cause the atleast one computer hardware processor to perform a method for training amulti-modal statistical model configured to receive input data frommultiple modalities including input data from a first modality and inputdata from a second modality different from the first modality. Themethod comprises: accessing unlabeled training data including unlabeledtraining data for the first modality and unlabeled training data for thesecond modality; accessing labeled training data including labeledtraining data for the first modality and labeled training data for thesecond modality; training the multi-modal statistical model in twostages, the multi-modal statistical model comprising multiple componentsincluding first and second encoders for processing input data for thefirst and second modalities, respectively, first and second modalityembeddings, a joint-modality representation, and a predictor, thetraining comprising: performing a first training stage at least in partby estimating values for parameters of the first and second modalityembeddings, and the joint-modality representation using aself-supervised learning technique and the unlabeled training data;performing a second training stage at least in part by estimating valuesfor parameters of the predictor using a supervised learning techniqueand the labeled training data; and storing information specifying themulti-modal statistical model at least in part by storing the estimatedvalues for parameters of the multiple components of the multi-modalstatistical model.

Some embodiments include at least one non-transitory computer-readablestorage medium storing processor-executable instructions that, whenexecuted by at least one computer hardware processor, cause the at leastone computer hardware processor to perform a method for training amulti-modal statistical model configured to receive input data frommultiple modalities including input data from a first modality and inputdata from a second modality different from the first modality. Themethod comprises: accessing unlabeled training data including unlabeledtraining data for the first modality and unlabeled training data for thesecond modality; accessing labeled training data including labeledtraining data for the first modality and labeled training data for thesecond modality; training the multi-modal statistical model in twostages, the multi-modal statistical model comprising multiple componentsincluding first and second encoders for processing input data for thefirst and second modalities, respectively, first and second modalityembeddings, a joint-modality representation, and a predictor, thetraining comprising: performing a first training stage at least in partby estimating values for parameters of the first and second modalityembeddings, and the joint-modality representation using aself-supervised learning technique and the unlabeled training data;performing a second training stage at least in part by estimating valuesfor parameters of the predictor using a supervised learning techniqueand the labeled training data; and storing information specifying themulti-modal statistical model at least in part by storing the estimatedvalues for parameters of the multiple components of the multi-modalstatistical model.

In some embodiments, training the multi-modal statistical model furthercomprises estimating values for parameters of the first and secondencoders prior to the first training stage.

In some embodiments, training the multi-modal statistical model furthercomprises estimating values for parameters of first and second decodersfor the first and second modalities, respectively, prior to the firsttraining stage.

In some embodiments, training the multi-modal statistical model furthercomprises estimating, during the first training stage, values forparameters of the first and second encoders jointly with estimatingvalues of parameters of the joint modality representation.

In some embodiments, training the multi-modal statistical model furthercomprises estimating, during the first training stage, values forparameters of a first decoder for the first modality and a seconddecoder for the second modality.

In some embodiments, performing the first training stage comprises:accessing a first data input in the unlabeled training data for thefirst modality; providing the first data input to the first encoder togenerate a first feature vector; identifying a second feature vectorusing the joint-modality representation, the first modality embeddingand the first feature vector; and providing the second feature vector asinput to a first decoder to generate a first data output.

In some embodiments, the method further comprises: comparing the firstdata output with the first data input; and updating at least one valueof at least one parameter of the joint-modality representation based onresults of the comparison.

In some embodiments, performing the first training stage comprises:accessing a first input in the unlabeled training data for the firstmodality; providing the first input data to the first encoder togenerate a first feature vector; identifying a second feature vectorusing the joint-modality representation, the second modality embeddingand the first feature vector; and providing the second feature vector asinput to a second decoder for the second modality to generate a secondoutput data.

In some embodiments, the first encoder is configured to output ad-dimensional vector, and wherein the joint-modality representationcomprises N m-dimensional vectors, and wherein the first modalityembedding comprises m*d weights.

In some embodiments, identifying the second feature vector using thejoint-modality representation, the first feature vector, and the firstmodality embedding comprises: projecting the joint modalityrepresentation to a space of the first modality by using the firstmodality embedding to obtain N d-dimensional vectors; and identifying,from among the N d-dimensional vectors in the joint-modalityrepresentation, a third feature vector most similar to the first featurevector according to a similarity metric; and generating the secondfeature vector by aggregating the first feature vector with the thirdfeature vector.

In some embodiments, identifying the second feature vector using thejoint-modality representation, the first feature vector, and the firstmodality embedding comprises: projecting the joint modalityrepresentation to a space of the first modality by using the firstmodality embedding to obtain N d-dimensional vectors; calculatingweights for at least some of the N d-dimensional vectors in the jointmodality representation according to a similarity between the at leastsome of the N d-dimensional vectors and the first feature vector; andgenerating the second feature vector by aggregating the first featurevector with the weighted sum of the at least some of the N d-dimensionalvectors weighted by the calculated weights.

In some embodiments, the multi-modal statistical model further comprisesfirst and second task embeddings, wherein training the multi-modalstatistical model further comprises estimating, during the secondtraining stage, values for parameters of the first and second taskembeddings jointly with estimating values of parameters of thepredictor.

In some embodiments, the first encoder comprises a neural network. Insome embodiments, the neural network is a convolutional neural network.In some embodiments, the neural network is a recurrent neural network.

In some embodiments, the first training stage comprises estimating thevalues for the parameters of the joint-modality representation using astochastic gradient descent technique. In some embodiments, the firsttraining stage further comprises estimating the values for theparameters of the first and second modality embeddings using thestochastic gradient descent technique.

In some embodiments, unlabeled training data for the first modalitycomprises images. In some embodiments, unlabeled training data for thesecond modality comprises text. In some embodiments, unlabeled trainingdata for the first modality comprises protein sequence data. In someembodiments, unlabeled training data for the second modality comprisesprotein family data, biological process ontology data, molecularfunction ontology data, cellular component ontology data, or taxonomicspecies family data.

In some embodiments, the method further comprises: accessing unlabeledtraining data for a third modality; accessing labeled training data forthe third modality; augmenting the multi-modal statistical model toinclude a third encoder for the third modality and a third modalityembedding; updating the multi-modal statistical model by: updatingvalues for parameters of the third modality embedding, and thejoint-modality representation using a self-supervised learning techniqueand the unlabeled training data for the third modality; and updatingvalues for parameters of the predictor using a supervised learningtechnique and the labeled training data for the third modality.

In some embodiments, the multi-modal statistical model is configured toreceive input data from a third modality different from the first andsecond modalities and further comprises a third modality embedding,wherein: accessing the unlabeled training data comprises accessingunlabeled training data for the third modality; accessing the labeledtraining data comprises accessing labeled training data for the thirdmodality; performing the first training stage further comprisesestimating values for parameters of the third modality embedding furtherbased on the unlabeled training data for the third modality; performingthe second training stage comprises estimating values for parameters ofthe predictor further based on the labeled training data for the thirdmodality.

Some embodiments include a method for performing a prediction task usinga multi-modal statistical model configured to receive input data frommultiple modalities including input data from a first modality and inputdata from a second modality different from the first modality. Themethod comprises obtaining information specifying the multi-modalstatistical model including values of parameters of each of multiplecomponents of the multi-modal statistical model, the multiple componentsincluding first and second encoders for processing input data for thefirst and second modalities, respectively, first and second modalityembeddings, a joint-modality representation, and a predictor; obtainingfirst input data for the first data modality; providing the first inputdata to the first encoder to generate a first feature vector;identifying a second feature vector using the joint-modalityrepresentation, the first modality embedding and the first featurevector; and generating a prediction for the prediction task using thepredictor and the second feature vector.

Some embodiments include a system for performing a prediction task usinga multi-modal statistical model configured to receive input data frommultiple modalities including input data from a first modality and inputdata from a second modality different from the first modality. Thesystem comprises: at least one computer hardware processor; and at leastone non-transitory computer-readable storage medium storing processorexecutable instructions that, when executed by the at least one computerhardware processor, causes the at least one computer hardware processorto perform: obtaining information specifying the multi-modal statisticalmodel including values of parameters of each of multiple components ofthe multi-modal statistical model, the multiple components includingfirst and second encoders for processing input data for the first andsecond modalities, respectively, first and second modality embeddings, ajoint-modality representation, and a predictor; obtaining first inputdata for the first data modality; providing the first input data to thefirst encoder to generate a first feature vector; identifying a secondfeature vector using the joint-modality representation, the firstmodality embedding and the first feature vector; and generating aprediction for the prediction task using the predictor and the secondfeature vector.

Some embodiments include at least one non-transitory computer-readablestorage medium storing processor executable instructions that, whenexecuted by the at least one computer hardware processor, causes the atleast one computer hardware processor to perform: obtaining informationspecifying the multi-modal statistical model including values ofparameters of each of multiple components of the multi-modal statisticalmodel, the multiple components including first and second encoders forprocessing input data for the first and second modalities, respectively,first and second modality embeddings, a joint-modality representation,and a predictor; obtaining first input data for the first data modality;providing the first input data to the first encoder to generate a firstfeature vector; identifying a second feature vector using thejoint-modality representation, the first modality embedding and thefirst feature vector; and generating a prediction for the predictiontask using the predictor and the second feature vector.

In some embodiments, the method further comprises: obtaining secondinput data for the second data modality; providing the second input datato the second encoder to generate a third feature vector; identifying afourth feature vector using the joint-modality representation, thesecond modality embedding and the third feature vector, whereingenerating the prediction for the prediction task is performed using thefourth feature vector.

In some embodiments, the multi-modal statistical model comprises firstand second task embeddings for the first and second modalities, andwherein generating the prediction for the prediction task furthercomprises: weighting the second feature vector using the first taskembedding; weighting the fourth feature vector using the second taskembedding; and generating the prediction for the prediction task usingthe weighted second and fourth feature vectors and the predictor.

In some embodiments, the method further comprises: providing theweighted second and fourth feature vectors to the predictor.

In some embodiments, the first encoder is configured to output ad-dimensional vector, and wherein the joint-modality representationcomprises N of m-dimensional vectors, and wherein the first modalityembedding comprises m×d weights.

In some embodiments, identifying the second feature vector using thejoint-modality representation, the first feature vector, and the firstmodality embedding comprises: projecting the joint modalityrepresentation to a space of the first modality by using the firstmodality embedding to obtain N d-dimensional vectors; identifying, fromamong the N d-dimensional vectors in the joint-modality representation,a third feature vector most similar to the first feature vectoraccording to a similarity metric; and generating the second featurevector by weighting dimensions of the third feature vector using weightsin the first modality embedding.

In some embodiments, identifying the second feature vector using thejoint-modality representation, the first feature vector, and the firstmodality embedding comprises: projecting the joint modalityrepresentation to a space of the first modality by using the firstmodality embedding to obtain N d-dimensional vectors; identifying, fromamong the N d-dimensional vectors in the joint-modality representation,a third feature vector most similar to the first feature vectoraccording to a similarity metric; and generating the second featurevector by aggregating the first feature vector and the third featurevector.

In some embodiments, identifying the second feature vector using thejoint-modality representation, the first feature vector, and the firstmodality embedding comprises: projecting the joint modalityrepresentation to a space of the first modality by using the firstmodality embedding to obtain N d-dimensional vectors; calculatingweights for at least some of the N d-dimensional vectors in the jointmodality representation according to a similarity between the at leastsome of the N d-dimensional vectors and the first feature vector; andgenerating the second feature vector as a weighted sum of the at leastsome of the N d-dimensional vectors weighted by the calculated weights.

In some embodiments, the first encoder comprises a neural network. Insome embodiments, the neural network is a convolutional neural network.In some embodiments, the neural network is a recurrent neural network.

In some embodiments, input data for the first modality comprises atleast one image. In some embodiments, input data for the second modalitycomprises text. In some embodiments, input data for the first modalitycomprises protein sequence data. In some embodiments, input data for thesecond modality comprises protein family data, biological processontology data, molecular function ontology data, cellular componentontology data, or taxonomic species family data.

It should be appreciated that all combinations of the foregoing conceptsand additional concepts discussed in greater detail below (provided suchconcepts are not mutually inconsistent) are contemplated as being partof the inventive subject matter disclosed herein.

BRIEF DESCRIPTION OF THE DRAWINGS

Various non-limiting embodiments of the technology will be describedwith reference to the following figures. It should be appreciated thatthe figures are not necessarily drawn to scale.

FIG. 1 is a diagram illustrating training of a knowledge base for astatistical model for a single modality using a self-supervised learningtechnique, in accordance with some embodiments of the technologydescribed herein.

FIG. 2A is a diagram illustrating a first training stage of amulti-modal statistical model using a self-supervised learningtechnique, in accordance with some embodiments of the technologydescribed herein.

FIG. 2B is a diagram illustrating a second training stage of themulti-modal statistical model using a supervised learning technique, inaccordance with some embodiments of the technology described herein.

FIG. 3 is a flowchart of an illustrative process for training amulti-modal statistical model using a two-stage training procedure, withthe first stage involving self-supervised learning and the second stageinvolving supervised learning, in accordance with some embodiments ofthe technology described herein.

FIG. 4 is a flowchart of an illustrative process 400 for using amulti-modal statistical model for a prediction task, in accordance withsome embodiments of the technology described herein.

FIG. 5 illustrates the performance of the multi-modal statistical modelon a prediction task relative to conventional techniques, in accordancewith some embodiments of the technology described herein.

FIGS. 6A and 6B illustrate encoders and decoders, in accordance withsome embodiments of the technology described herein.

FIG. 7 shows components of an illustrative computer system on which someembodiments of the technology described herein may be implemented.

DETAILED DESCRIPTION

A statistical model configured receive, as input, and process, data frommultiple modalities may be referred to as a multi-modal statisticalmodel. The inventors have developed a new class of multi-modalstatistical models by developing novel techniques for integratingmultiple individual statistical models, each designed to process data ina different respective modality, to generate multi-modal statisticalmodels. The techniques described herein may be used to integratemultiple deep learning models trained for different modalities and/orany other suitable types of statistical models. The techniques developedby the inventors address drawbacks of conventional techniques forbuilding multi-modal statistical models. By addressing these drawbacks,the inventors have developed technology that improves upon conventionalmachine learning systems and the computer technology used to implementthem.

Conventional machine learning techniques for training a multi-modalstatistical model require that the multi-modal statistical model betrained “synchronously” using linked data from each of the multiplemodalities, whereby each piece of training data includes data from eachof the modalities the statistical model is being trained to process. Therequirement for such concurrent training is a severe limitation andprevents the design of multi-modal statistical models that can receiveand process data from more than a handful of (e.g., 2 or 3) modalities,whereas multi-modal statistical models that can input process a muchgreater number of data modalities are needed, especially in fields suchas medicine and biology.

Synchronous training is a severe limitation because it requirescollecting linked data—each piece of training data for one modality musthave a corresponding piece of training data in every other modality thatthe multi-modal statistical model is being trained to process.Collecting such training data is prohibitively expensive and extremelytime-consuming, requiring hundreds or thousands of man hours to collectand label the data. Even if concurrent training were possible and linkeddata were available for two data modalities, if at a later time new datafor another data modality were obtained, the new data would have to belinked (again time consuming and expensive) to the existing data, andthe entire statistical model would have to be re-trained. In sum,synchronous training makes it impractical, and near-impossible inpractice, to generate and update multi-modal statistical models for morethan a small number (i.e., 2 or 3) modalities.

The techniques developed by the inventors and described herein allow forefficiently creating and updating of multi-modal statistical modelswithout requiring that training be performed synchronously using linkeddata from each of the multiple modalities that the statistical model isbeing trained to process. In contrast to conventional techniques, theinventors have developed an approach that allows for asynchronoustraining and updating of multi-modal statistical models. Theasynchronous training is enabled by the innovative shared code-bookarchitecture described herein. In this architecture, individualstatistical models, previously trained for processing data in respectivemodalities, are integrated by coupling their respective latentrepresentations to a joint modality representation, which allowsinformation among the individual models to be shared.

The inventors have not only developed an innovative architecture forintegrating individual statistical models, but have also specified novelalgorithms for asynchronously training components of this architectureusing training data from each of multiple modalities, and updating theparameters of the trained components as additional data becomesavailable. The techniques described herein can be applied to training amulti-modal statistical model to receive and process data for anysuitable number of data modalities (e.g., two, three, four, five, six,seven, eight, nine, ten, eleven, twelve, thirteen, fourteen, fifteen,sixteen, etc.). As described below with reference to FIG. 5 , theinventors have used the new techniques to generate a multi-modalstatistical model for processing data arising in six differentmodalities (for the problem of protein structure prediction), whichwould not be possible with conventional techniques.

Utilizing asynchronous training not only provides an improvement overconventional techniques in that it, for the first time, enablesgenerating multi-modal statistical models for any suitable number ofdata modalities, but also improves the computer technology used to trainand deploy such machine learning systems. In particular, the multi-modalstatistical models described herein may be trained with less trainingdata (because linked training data instances across all modalities arenot required), which in turn means that fewer computing resources needto be used to train and deploy such models. Specifically, less processorpower and time is needed, less memory is needed, and less networkingresources (e.g., network bandwidth) is needed for the transmission ofsuch data, all of which directly improves computer functionality.

The techniques developed by the inventors may be referred to, at times,as the “UNITY” framework, as they allow for the efficient unification ofstatistical models built for different data modalities through thetechniques of training and using multi-modal statistical modelsdeveloped by the inventors and described herein.

Accordingly, some embodiments, provide for techniques for training amulti-modal statistical model configured to receive input data frommultiple modalities including input data from a first modality and inputdata from a second modality different from the first modality. Thetechniques include: (1) accessing unlabeled training data includingunlabeled training data for the first modality and unlabeled trainingdata for the second modality; (2) accessing labeled training dataincluding labeled training data for the first modality and labeledtraining data for the second modality; (3) training the multi-modalstatistical model in two stages, the multi-modal statistical modelcomprising multiple components including first and second encoders forprocessing input data for the first and second modalities, respectively,first and second modality embeddings, a joint-modality representation,and a predictor, the training comprising: (A) performing a firsttraining stage at least in part by estimating values for parameters ofthe first and second modality embeddings, and the joint-modalityrepresentation using a self-supervised learning technique and theunlabeled training data; (B) performing a second training stage at leastin part by estimating values for parameters of the predictor using asupervised learning technique and the labeled training data; and (4)storing information specifying the multi-modal statistical model atleast in part by storing the estimated values for parameters of themultiple components of the multi-modal statistical model.

In some embodiments, the parameters of the first and second encoders maybe estimated prior to the first training stage of the multi-modalstatistical model. This may the case when individual statistical modelsbeing integrated have been previously trained and the parameters oftheir respective encoders have been estimated. In other embodiments, theparameters of the encoders may be estimated for the first time and/orupdated during the training of the multi-modal statistical model.Similarly, the first and second decoders may be trained prior to orduring the training of the multi-modal statistical modal.

In some embodiments, the joint modality representation may be acode-book including N m-dimensional vectors. Each individual statisticalmodel being integrated may be configured to: generate a latentrepresentation of its input and use this latent representation toidentify a similar vector or vectors in the joint modalityrepresentation. In turn, the identified vector(s) may be used togenerate a new set of features that can be used for a prediction task.In this way, features generated for one modality may be updated toreflect, through the use of a common code-book, information gathered ina different modality.

In some embodiments, performing the first training stage comprises: (A)accessing a first data input in the unlabeled training data for thefirst modality; (B) providing the first data input to the first encoderto generate a first feature vector; (C) identifying a second featurevector using the joint-modality representation, the first modalityembedding and the first feature vector; (D) providing the second featurevector as input to a first decoder to generate a first data output. Thefirst data output may then be compared with the first data input, andone or more parameter values of the joint-modality representation may beupdated based on results of the comparison (e.g., using stochasticgradient descent).

In some embodiments, identifying the second feature vector using thejoint-modality representation, the first feature vector, and the firstmodality embedding comprises: (A) projecting the joint modalityrepresentation to a space of the first modality by using the firstmodality embedding to obtain N d-dimensional vectors; (B) calculatingweights for at least some of the N d-dimensional vectors in the jointmodality representation according to a similarity between the at leastsome of the N d-dimensional vectors and the first feature vector; and(C) generating the second feature vector by aggregating the firstfeature vector with the weighted sum of the at least some of the Nd-dimensional vectors weighted by the calculated weights.

In some embodiments, the multi-modal statistical model being trainedfurther comprises first and second task embeddings, wherein training themulti-modal statistical model further comprises estimating, during thesecond training stage, values for parameters of the first and secondtask embeddings jointly with estimating values of parameters of thepredictor.

In some embodiments, the first encoder may be a neural network such as aconvolutional neural network, a recurrent neural network, or any othersuitable type of statistical model.

In some embodiments, the unlabeled training data for the first modalitycomprises images and the unlabeled training data for the second modalitycomprises text. In some embodiments, the unlabeled training data for thefirst modality comprises protein sequence data and the unlabeledtraining data for the second modality comprises protein family data,biological process ontology data, molecular function ontology data,cellular component ontology data, or taxonomic species family data.

Some embodiments include techniques for performing a prediction taskusing a multi-modal statistical model configured to receive input datafrom multiple modalities including input data from a first modality andinput data from a second modality different from the first modality. Thetechniques include: (A) obtaining information specifying the multi-modalstatistical model including values of parameters of each of multiplecomponents of the multi-modal statistical model, the multiple componentsincluding first and second encoders for processing input data for thefirst and second modalities, respectively, first and second modalityembeddings, a joint-modality representation, and a predictor; (B)obtaining first input data for the first data modality; (C) providingthe first input data to the first encoder to generate a first featurevector; (D) identifying a second feature vector using the joint-modalityrepresentation, the first modality embedding and the first featurevector; and (E) generating a prediction for the prediction task usingthe predictor and the second feature vector.

In some embodiments, the techniques may further include: (A) obtainingsecond input data for the second data modality; (B) providing the secondinput data to the second encoder to generate a third feature vector; (C)identifying a fourth feature vector using the joint-modalityrepresentation, the second modality embedding and the third featurevector. Generating the prediction for the prediction task may beperformed using the second feature vector and the fourth feature vector.

In some embodiments, the multi-modal statistical model may comprisesfirst and second task embeddings for the first and second modalities,and generating the prediction for the predict task may include:weighting the second feature vector using the first task embedding;weighting the fourth feature vector using the second task embedding; andgenerating the prediction for the prediction task using the weightedsecond and fourth feature vectors and the predictor.

It should be appreciated that the techniques introduced above anddiscussed in greater detail below may be implemented in any of numerousways, as the techniques are not limited to any particular manner ofimplementation. Examples of details of implementation are providedherein solely for illustrative purposes. Furthermore, the techniquesdisclosed herein may be used individually or in any suitablecombination, as aspects of the technology described herein are notlimited to the use of any particular technique or combination oftechniques.

FIG. 1 is a diagram illustrating training of a knowledge base for astatistical model 100 for a single modality using a self-supervisedlearning technique, in accordance with some embodiments of thetechnology described herein. The statistical model 100 includes a numberof components having respective parameters including encoder 104,decoder 110, and memory 105 representing a knowledge base.

In this example, it is assumed that the encoder 104 and decoder 110 havebeen previously trained as shown by the fill pattern having diagonallines extending downward from left to right and that the memory 105 isnot yet trained, as shown by the fill pattern having diagonal linesextending upward from left to right. However, as described in moredetail below, in some embodiments, the individual statistical models maybe trained for the first time or at least updated during training of themulti-modal statistical model.

In some embodiments, encoder 104 may be configured to receive input andoutput a latent representation (which may have a lower dimensionalitythan the dimensionality of the input data) and the first decoder may beconfigured to reconstruct the input data from the latent representation.In some embodiments, the encoder and decoder may be part of anauto-encoder. In some embodiments, the statistical model 100 may beneural network model and the encoder 104 and the decoder 110 may includeone or more neural network layers such that the parameters of theencoder 104 and decoder 110 include weights for each of the neuralnetwork layers. Though it should be appreciated that the encoder 104 anddecoder 110 are not limited to being neural networks and may be anyother suitable type of statistical model.

In some embodiments, parameters values for the memory 105 may beestimated using self-supervised learning, so that the output ofstatistical model 100 reproduces the inputs to the statistical model 100as closely as possible. Accordingly, in some embodiments, duringtraining, output of the statistical model 100 is compared to the inputand the parameter values of the memory 105 are updated iteratively,based on a measure of distance between the input and the output, usingstochastic gradient descent (with gradients calculated usingbackpropagation when the encoder and decoder are neural networks) or anyother suitable training algorithm.

For example, in some embodiments, training data may be provided as input102 to the first encoder 104. Encoder 104 generates, based on the input102, the first feature representation 106. The feature representation106 is used to obtain, using the memory 105, a second featurerepresentation 108. In some embodiments, the memory 105 may store aplurality of vectors having the same dimensionality as that of featurerepresentation 106. For example, the feature representation 108 may be ad-dimensional vector and the memory 105 may store N d-dimensionalvectors. In some embodiments, the second feature representation 108 maybe obtained by selecting, from among the vectors in memory 105, thevector most similar (according to a suitable measure of similarity suchas cosine similarity, Euclidean distance, etc.) to the first featurerepresentation 106 and adding the selected vector to the featurerepresentation 106 via aggregation operation 107 (which may besummation, multiplication, arithmetic averaging, geometric averaging, orany other suitable operation). In some embodiments, the second featurerepresentation 108 may be generated by aggregating with featurerepresentation 106 a weighted linear combination of the vectors inmemory 105, with the weight for each vector being proportional to thedistance between the vector and the feature representation 106. Thesecond feature representation is provided as input to decoder 110. Inturn, the output of decoder 110 may be compared with the input providedto the encoder 104, and at least some of the parameter values of thememory 105 may be updated based on the difference between the input toencoder 104 and the output of decoder 110.

Although in the embodiment explained with reference to FIG. 1 , it wasassumed that encoder 104 and decoder 110 have been trained, in otherembodiments, the parameter values of encoder 104 and decoder 110 may beestimated for the first time and/or updated at the same time as theparameter values of memory 105 are being estimated.

The illustrative example of FIG. 1 is helpful for understanding thetechniques developed by the inventors for integrating multiplepreviously-trained statistical models into a single multi-modalstatistical model. In particular, as described herein, the multi-modalstatistical model allows for sharing of information among differentmodalities through a joint modality representation. Like the memory 105,which is accessed during training and use of statistical model 100 for asingle modality, the joint modality representation (e.g., knowledge base230 shown in FIGS. 2A and 2B), is accessed during training and use ofmulti-modal statistical models (e.g., model 250) described herein.

As described herein, when the joint modality representation is accessedto perform calculations for one modality, its contents may be firstprojected to that modality using a modality embedding. Such modalityprojections forms part of the multi-modal statistical models describedherein.

As described in connection with FIG. 1 , the single-modality statisticalmodel 100 includes memory 105, which may be trained usingself-supervised learning using previously-trained encoder 104, decoder110, and training data (which need not be labeled with respect to anyclassification task). The multi-modal statistical model developed by theinventors (e.g., multi-modal statistical model 250) includes a jointmodality representation (e.g., knowledge base 230) and multiple modalityembeddings (e.g., modality embeddings 232), which may be trained usingself-supervised learning, as described herein including with referenceFIGS. 2A, 2B, and 3 , and used for prediction, as described hereinincluding with reference to FIGS. 2B and 4 .

In some embodiments, the multi-modal statistical model developed by theinventors may be trained using a two-stage training procedure. The firsttraining stage is performed using a self-supervised training techniqueand involves learning parameters of the joint modality representationand modality embeddings. The second stage is performed using asupervised training technique and involves learning parameters of apredictor (for an appropriate prediction task) and task embeddings.FIGS. 2A and 2B illustrate which components of the multi-modalstatistical model are learned in each of these two stages, in someembodiments.

FIG. 2A is a diagram illustrating a first training stage of amulti-modal statistical model using a self-supervised learningtechnique, in accordance with some embodiments of the technologydescribed herein. As shown in FIG. 2A, the statistical model includes anumber of components having respective parameters including an encoder204 for the first modality, an encoder 214 for the second modality, aknowledge base 230, and modality embeddings 232, which includes amodality embedding for each of the first and second modalities.Additionally, as shown in FIG. 2A, the training environment 200 includesdecoder 210 for the first modality and the decoder 220 for the secondmodality. These decoders are not part of the multi-modal statisticalmodel, rather the decoders are used for training the multi-modalstatistical model in the self-supervised training stage; they are notused for prediction as may be seen from FIG. 2B.

In the embodiment illustrated in FIG. 2A, it is assumed that theencoders 204 and 214, and the decoders 210 and 220, have been previouslytrained as shown by the fill pattern having diagonal lines extendingdownward from left to right, and that the knowledge base 230 and themodality embeddings 232 are not yet trained, as shown by the fillpattern having diagonal lines extending upward from left to right.However, as described herein in some embodiments, one or more of theencoders and decoders may be trained for the first time or at leastupdated during training of the multi-modal statistical model.

In some embodiments, each of encoder 204, encoder 214, decoder 210 anddecoder 220 may be a respective neural network comprising one or moreneural network layers. The layers may include one or more convolutionallayers, one or more pooling layers, one or subsampling layers, one ormore fully connected layers, and/or any other suitable layer(s).However, none of encoders 204 and 214, and decoders 210 and 220 arelimited to be a neural network model and may be any other suitable typeof statistical model(s), as aspects of the technology described hereinare not limited in this respect.

In some embodiments, the knowledge base 230 (which is an example of ajoint modality representation) may include N m-dimensional vectors.These vectors may be stored and/or represented using a matrix (e.g., anN×m matrix) or any other suitable data structure(s), as aspects of thetechnology described herein are not limited in this respect.

In some embodiments, each modality embedding may be configured toproject the knowledge base 230 into the respective modality space. Forexample, in some embodiments, the modality embedding (of modalityembeddings 232) for the first modality may be used to project, usingprojection operation 237, the knowledge base 230 to the first modalityin order to obtain a first modality view 238 of the knowledge base 230.The projection operation may make use of weights 234 part of themodality embedding for the first modality. As another example, in someembodiments, the modality embedding (of modality embeddings 232) for thesecond modality may be used to project, using projection operation 239,the knowledge base 230 to the second modality in order to obtain asecond modality view 240 of the knowledge base 230. The projectionoperation may make use of weights 236 part of the modality embedding forthe second modality.

In some embodiments, each modality embedding may be configured toproject the knowledge base 230 into the respective modality space suchthat the dimensionality of the vectors in the projected knowledge basematch the dimensionality of the latent representation in that modalityspace. For example, suppose the knowledge base 230 includes Nm-dimensional vectors, with N=512 and m=64, and that the latentrepresentation generated by the encoder for the first modality is ad-dimensional vector with d=10. In this example, the modality embeddingfor the first modality may be an m×d (a 64×10) matrix, which whenapplied to the 512×64 knowledge base 230 generates a 512×10 view of theknowledge base 230 for the first modality. Suppose further that thelatent representation generated by the encoder for the second modalityis a p-dimensional vector with p=12. Then, the modality embedding forthe first modality may be an m×p (a 64×12) matrix, which when applied tothe 512×64 knowledge base 230 generates a 512×12 view of the knowledgebase 230 for the second modality. As may be appreciated from theforegoing example, the modality embeddings, among other things, allowfor the integration of statistical models for different modalities in asituation where the dimensionality of the latent representations in notthe same (e.g., 10-dimensional in one modality and 12-dimensional inanother modality).

Aspects of the first (self-supervised) training stage of the multi-modalstatistical model are described in more detail below with reference toFIG. 3 .

FIG. 2B is a diagram illustrating a second training stage of themulti-modal statistical model 250 using a supervised learning technique,in accordance with some embodiments of the technology described herein.As shown in FIG. 2B, the multi-modal statistical model 250 includespredictor 252 for prediction task 256 and task embeddings 254.

In the embodiment illustrated in FIG. 2B, it is assumed that theencoders 204 and 214, the decoders 210 and 220, the knowledge base 230,and the modality embeddings 232 have been previously trained as shown bythe fill pattern having diagonal lines extending downward from left toright, and that the predictor 252 and task embeddings 254, as shown bythe fill pattern having diagonal lines extending upward from left toright. However, as described herein, in some embodiments, one or more ofthe encoders, decoders, modality embeddings, and joint modalityrepresentation may be trained for the first time or at least updatedduring the second stage of training of the multi-modal statisticalmodel.

In some embodiments, the predictor 252 may be of any suitable typestatistical model mapping input features to an output (e.g., a discretelabel in the case of a classifier or continuous variable in the case ofa regressor). For example, the predictor 252 may comprise a linear model(e.g., a linear regression model), a generalized linear model (e.g.,logistic regression, probit regression), a neural network or othernon-linear regression model, a Gaussian mixture model, a support vectormachine, a decision tree model, a random forest model, a Bayesianhierarchical model, a Markov random field, and/or any other suitabletype of statistical model, as aspects of the technology described hereinare not limited in this respect.

In some embodiments, the task embeddings 254 may be used to weight, viaoperations 256 and 258, the contribution of features from the first andsecond modalities. For example, as shown in FIG. 2B, the featurerepresentation 208 may be weighted, via operation 256, using the taskembedding for the first modality and the feature representation 218 maybe weighted, via operation 258, using the task embedding for the secondmodality. These weighted feature representations may then be aggregated(e.g., as a weighted sum or product) via operation 260 to generate inputfor the predictor 252. The weighting induced by a task embedding to afeature representation may be a point-wise multiplicative weighting(e.g., a Hadamard product).

Aspects of the second (supervised) training stage of the multi-modalstatistical model are described in more detail below with reference toFIG. 3 .

Training Multi-Modal Statistical Models

FIG. 3 is a flowchart of an illustrative process 300 for training amulti-modal statistical model using a two-stage training procedure, withthe first stage involving self-supervised learning and the second stageinvolving supervised learning, in accordance with some embodiments ofthe technology described herein. The process 300 may be performed by anysuitable computing device(s). For example, the process 300 may beperformed by one or more graphics processing units (GPUs), one or morecomputing device(s) provided by a cloud computing service, and/or anyother suitable computing device(s), as aspects of the technologydescribed herein are not limited in this respect.

In the embodiment illustrated in FIG. 3 and described below, process 300is used to train a multi-modal statistical model configured to receiveinput from two modalities a first modality and a second modality.However, it should be appreciated that the process 300 may be used totrain a multi-modal statistical model configured to receive input fromany suitable number of modalities (e.g., three, four, five, six, seven,eight, nine, ten, eleven, twelve, etc.), as aspects of the technologydescribed herein are not limited in this respect.

In this example, it is assumed that prior to the start of the process300, individual statistical models have been trained for the first andsecond modalities. In particular, it is assumed that a first statisticalmodel, including a first encoder and a first decoder, has been trainedfor the first modality and that a second statistical model, including asecond encoder and a second decoder, has been trained for the secondmodality. The first statistical model may be an auto-encoder typestatistical model having been trained using data in the first modality.The second statistical model may be an auto-encoder type statisticalhaving been trained using data in the second modality. However, asdescribed in more detail below, in some embodiments, the individualstatistical models may be trained for the first time or at least updatedduring training of the multi-modal statistical model.

In some embodiments, the multi-modal statistical model being trainedduring execution of process 300 may comprise an encoder component foreach of the modalities, a joint modality representation component, amodality embedding component for each of the modalities, a predictorcomponent, and a task embedding component for each of the modalities,and process 300 may be used to estimate parameter values for each of oneor more of these components. For example, the multi-modal statisticalmodel 250 of FIG. 2B comprises encoder 204, encoder 214, knowledge base230, modality embeddings 232, predictor 252, and task embeddings 254 andparameters of the components 230, 232, 252, and 254 may be estimated aspart of process 300. It should be appreciated that the decoders for eachof multiple modalities (which may be part of the individual statisticalmodels being integrated) may not be part of the multi-modal statisticalmodel. Notwithstanding, such decoders may be used to train themulti-modal statistical model, in a self-supervised learning stage, asdescribed in more detail below.

Process 300 begins at act 302, where the parameters of a first trainedstatistical model for a first modality and parameters of a secondtrained statistical model for a second modality are accessed. Theparameters may be accessed from local storage, over a network fromremote storage, or any other suitable source.

In some embodiments, the first trained statistical model may include anauto-encoder and may comprise a first encoder and a first decoder, eachhaving a respective set of parameters, which may be accessed at act 302.The first encoder may be configured to receive, as input, data havingthe first modality and output a latent representation (which may have alower dimensionality than the dimensionality of the input data) and thefirst decoder may be configured to reconstruct the input data from thelatent representation. In some embodiments, the first trainedstatistical model may be a neural network (e.g., a feedforward neuralnetwork, a convolutional neural network, a recurrent neural network, afully connected neural network, etc.) and the first encoder and thefirst decoder may include one or more neural network layers such thatthe parameters of the first encoder and decoder include weights for eachof the neural network layers. Though it should be appreciated that thefirst trained statistical model is not limited to being a neural networkand may be any other suitable statistical model.

In some embodiments, the second trained statistical model may include anauto-encoder and may comprise a second encoder and a second decoder,each having a respective set of parameters, which may be accessed at act302. The second encoder may be configured to receive, as input, datahaving the second modality and output a latent representation (which mayhave a lower dimensionality than the dimensionality of the input data)and the second decoder may be configured to reconstruct the input datafrom the latent representation. In some embodiments, the second trainedstatistical model may be a neural network (e.g., a feedforward neuralnetwork, a convolutional neural network, a recurrent neural network, afully connected neural network, etc.) and the second encoder and thesecond decoder may include one or more neural network layers such thatthe parameters of the first encoder and decoder include weights for eachof the neural network layers. Though it should be appreciated that thesecond trained statistical model is not limited to being a neuralnetwork and may be any other suitable statistical model.

In some embodiments, the first encoder and the second encoder aredifferent from one another since they are configured to receive data ofdifferent modalities. In such embodiments, the first and second decodersare different from each other. In some such embodiments, when theencoders are each implemented as neural networks, the neural networkarchitecture for the encoders is different (e.g., different numbers oflayers, different types of layers, different dimensionality of layers,different non-linearities, etc.). As one example, the first encoder maybe configured to receive, as input, an image and produce a latentrepresentation of the image and the second encoder may be configured toreceive, as input text and produce a latent representation of the text.As another example, the first encoder may be configured to receive andproduce a latent representation of protein sequence data, and the secondencoder may be configured to receive, and produce a latentrepresentation of protein family data. As yet another example, the firstencoder may configured to receive and produce a latent representation ofa medical image of a first type (e.g., ultrasound) and the secondencoder may be configured to receive and produce a latent representationof a medical images of a second type different from the first type(e.g., MRI image).

In some embodiments, the latent representation produced at the output ofthe first encoder may have the same dimensionality as the latentrepresentation produced at the output of the second encoder. Forexample, as described in more detail below, the first encoder mayreceive as input a representation of a protein sequence (e.g., a 20×1024one-hot-encoded protein sequence) and return a 10×1 latentrepresentation. In this same example, the second encoder may receive asinput biological process input (which, for example, may beone-hot-encoded as a 24,937-dimensional vector) and return a 10×1 latentrepresentation. However, it is not a requirement that the latentrepresentations be of the same dimension, as using different modalityembeddings provides for the additional flexibility, whereby latentrepresentations for different modalities have different dimensions.

FIG. 2A illustrates one example of the parameters that may be accessedat act 302. In particular, parameters of encoder 204 (first encoder),decoder 210 (first decoder), encoder 214 (second encoder), and decoder218 may be accessed at act 302.

Next, process 300 proceeds to act 303, where unlabeled training data isaccessed for each the first and second modalities. The unlabeledtraining data accessed at act 303 may be used for the first stage oftraining the multi-modal statistical model using self-supervisedlearning at act 306. As part of the first training stage, the unlabeledtraining data may be used to estimate parameters of one or morecomponents of the multi-modal statistical model, which components allowfor integrating the first and second statistical models (whoseparameters were accessed at act 302). For example, the multi-modalstatistical model (e.g., model 250 shown in FIG. 2B) may include a jointmodality representation (e.g., knowledge base 230), a first modalityembedding, (e.g., part of modality embeddings 232) and a second modalityembedding (e.g., part of modality embeddings 232), and the unlabeledtraining data may be used to estimate parameters of the joint modalityrepresentation, the first modality embedding, and the second modalityembedding during act 306.

It should be appreciated that, while the unlabeled training dataaccessed at act 303 includes training data for each of the first andsecond modalities, these data need not have been gathered synchronouslyor in a coordinated fashion. The unlabeled training data for the firstmodality may have been generated independently from the unlabeledtraining data for the second modality. The unlabeled training data fordifferent modalities may be generated at different times by differententities and/or may be stored in different databases. There may be moretraining data for the first modality than for the second or vice versa.Training data for the first and second modality need not be paired—thereneed not be a one-to-one correspondence. In some embodiments, thetraining data obtained at act 303 may be labeled, but the labels may bediscarded or ignored when the training data is used during the firsttraining stage at act 306.

Next, process 300 proceeds to act 304, where labeled training data isaccessed for the first and second modalities. The labeled training dataaccessed at act 304 may be used for the second stage of training themulti-modal statistical model using supervised learning at act 308. Aspart of the second training stage, the labeled training data may be usedto estimate parameters of one or more components of the multi-modalstatistical model, which components allow for integrating the first andsecond statistical models (whose parameters were accessed at act 302)and using these models to perform a prediction task. For example, themulti-modal statistical model (e.g. model 250 shown in FIG. 2B) mayinclude a predictor (e.g., predictor 252), a first task embedding,(e.g., part of task embeddings 254) and a second modality embedding(e.g., part of task embeddings 254), and the labeled training data maybe used to estimate parameters of the predictor, the first taskembedding, and/or the second modality embedding during act 308.

While the labeled training data accessed at act 304 includes trainingdata for each of the first and second modalities, these data need nothave been gathered synchronously or in a coordinated fashion. Thelabeled training data for the first modality may have been generatedindependently from the labeled training data for the second modality.The labeled training data for different modalities may be generated atdifferent times by different entities and/or may be stored in differentdatabases. There may be more training data for the first modality thanfor the second or vice versa. Training data for the first and secondmodality need not be paired—there need not be a one-to-onecorrespondence.

Next, process 300 proceeds to act 305 where the multi-modal statisticalmodel is trained using a two-stage procedure. Initially, at act 306, theunlabeled data obtained at act 303 is used to estimate parameter valuesfor one or more components of the multi-modal statistical model using aself-supervised learning technique. Next, at act 308, the labeled dataobtained at act 304 is used to estimate parameter values for one or moreadditional components of the multi-modal statistical model using asupervised learning technique. Each of these acts is described infurther detail below.

In some embodiments, act 306 may comprise estimating parameter valuesfor one or more components of the multi-modal statistical model using aself-supervised learning technique. In some embodiments, the parametersof the joint modality representation (e.g., knowledge base 230 in theexample of FIG. 2B) may be estimated at act 306. Additionally, in someembodiments, parameters of one or more modality embeddings (e.g., one ormore of modality embeddings 232) may be estimated at act 306.

In some embodiments, the parameter values estimated as part of act 306may be estimated using self-supervised learning. Training a statisticalmodel using self-supervised learning may involve training thestatistical model to reproduce inputs at the outputs. Accordingly, insome embodiments, a particular piece of data may be provided as input tothe statistical model and the output of the statistical model may becompared to the very same particular piece of data. In turn, one or morevalues of the parameters of the statistical model may be updated (e.g.,using stochastic gradient descent or any other suitable trainingalgorithm) based on the difference between the output of the statisticalmodel and the particular piece of data provided to the statisticalmodel, which difference provides a measure of how well the output of thestatistical model, when operated with its current set of parametervalues, reproduces the input.

In some embodiments, the unlabeled training data accessed at act 303 maybe used to estimate parameter values of the joint modalityrepresentation and the modality embeddings in the multi-modalstatistical model. The parameter values may be estimated using aniterative learning algorithm such as, for example, stochastic gradientdescent. The iterative learning algorithm may involve providing at leastsome of the unlabeled training data as input to the encoders of themulti-modal statistical model, generating output using the respectivedecoders, comparing the input with the generated output, and updatingthe parameters values of the joint modality representation and/or themodality embeddings based on the difference between the input andoutput.

For example, in some embodiments, training data of a first modality maybe provided as input to a first encoder for the first modality (e.g.,encoder 204). The output of the first encoder (e.g., featurerepresentation 206), the joint modality representation (e.g., knowledgebase 230), and the first modality embedding (e.g., one of modalityembeddings 232), may be used to generate input (e.g., featurerepresentation 208) to a first decoder for the first modality (e.g.,decoder 210). In turn, the output of the decoder 210 may be comparedwith the input provided to the first encoder and at least some of theparameter values of the joint modality representation and/or the firstmodality embedding may be updated based on the difference between theinput to the first encoder and the output of the first decoder.

In this example, generating the input to the first decoder from theoutput of the first encoder may include: (1) projecting the jointmodality representation to the space of the first modality to obtain aplurality of projected vectors; (2) calculating a distance (e.g., acosine distance and/or any other suitable type of distance measure)between each of the plurality of projected vectors and the output of thefirst encoder and using these distances to calculate weights for theprojected vectors (e.g., by using a soft-max weighting); and (3)generating input to the first decoder by aggregating, with the output ofthe first encoder, a weighted sum of the projected vectors weighted bythe calculated weights. For example, the joint modality representationmay include N m-dimensional vectors (which may be represented and/orstored as an N×m matrix), and projecting the joint modalityrepresentation using a first modality projection, which may berepresented as an m×d to the first modality may produce N d-dimensionalvectors (which may be represented an as an N×d matrix). The distancebetween the output of the first encoder (e.g., feature representation206 shown in FIG. 2A) and each of the N d-dimensional vectors may becalculated and used to obtain weights for each of the N d-dimensionalvectors. Then the input to the first decoder (e.g., featurerepresentation 208) may be calculated as an aggregation 207 (e.g., sum,product, arithmetic average, geometric average) of the featurerepresentation 206 with the weighted sum of the N d-dimensional vectors,with the vectors being weighted by the calculated weights. In otherembodiments, the input the first decoder may be the sum of the output ofthe first encoder and the N d-dimensional vector closest to the outputof the first encoder according to a suitably-chosen distance measure(e.g., cosine distance) rather than a weighted average of multipled-dimensional vectors in the projected joint modality representation, asaspects of the technology described herein are not limited in thisrespect. In yet other embodiments, the input to the first decoder may bethe weighted sum of the N d-dimensional vectors (calculated as discussedabove) or the vector most similar to the output of the first encoder(identified as described above), but without being aggregated with theoutput of the first encoder.

As another example, in some embodiments, training data of a secondmodality may be provided as input to a second encoder for the secondmodality (e.g., encoder 214). The output of the second encoder (e.g.,feature representation 216), the joint modality representation (e.g.,knowledge base 230), and the second modality embedding (e.g., one ofmodality embeddings 232), may be used to generate input (e.g., featurerepresentation 218) to a second decoder for the second modality (e.g.,decoder 220) using aggregation operation 217. In turn, the output of thedecoder 220 may be compared with the input provided to the secondencoder and at least some of the parameter values of the joint modalityrepresentation and/or the second modality embedding may be updated basedon the difference between the input to the second encoder and the outputof the second decoder.

In some embodiments, act 308 may comprise estimating parameter valuesfor one or more components of the multi-modal statistical model using asupervised learning technique. In some embodiments, the parameters of apredictor (e.g., predictor 252 in the example of FIG. 2B) may beestimated at act 308. Additionally, in some embodiments, parameters ofone or more task embeddings (e.g., one or more of task embeddings 254)may be estimated at act 308.

In some embodiments, the parameter values estimated as part of act 306may be estimated using supervised learning based on the labeled trainingdata accessed at act 304. In some embodiments, a particular piece ofdata may be provided as input to the statistical model and the output ofthe statistical model may be compared to the label for the particularpiece of data. In turn, one or more values of the parameters of thestatistical model may be updated (e.g., using stochastic gradientdescent or any other suitable training algorithm) based on thedifference between the output of the statistical model and the label forthe particular piece of data provided to the statistical model, whichdifference provides a measure of how well the output of the statisticalmodel, when operated with its current set of parameter values,reproduces the provided labels.

In some embodiments, the loss (or cost) function used during the secondtraining stage may be selected depending on the type of task for whichthe predictor component of the multi-modal statistical model is beingtrained. For example, if the task involves multi-label exclusiveclassification, cross-entropy loss may be used. As another example, ifthe task involves prediction of a continuous distribution,Kullback-Leibler divergence may be used at the loss function.

In some embodiments, during performance of the second stage, theparameter values estimated during the first training stage may be fixed.For example, after parameter values for the joint modalityrepresentation and modality embeddings are estimated during the firsttraining stage, these values may remain fixed during the second trainingstage, while parameter values for the predictor and task embeddings arebeing estimated during the second training stage.

After act 308 completes, thereby completing act 305, the trainedmulti-modal statistical model may be stored, at act 310, for subsequentuse. Storing the trained multi-modal statistical model comprises storingparameter values for one or more components of the multi-modalstatistical model. In some embodiments, storing the trained multi-modalstatistical model comprises storing parameter values estimated duringact 305 for one or more of the following components: joint modalityrepresentation, first modality embedding, second modality embedding,predictor, first task embedding, and the second task embedding. Theparameter values may be stored in any suitable format, as aspects of thetechnology described herein are not limited in this respect. Theparameter values may be stored using one or multiple computer-readablestorage mediums (e.g., one or more memories).

It should be appreciated that the process 300 is illustrative and thatthere are variations. For example, although process 300 is describedwith reference to training a multi-modal statistical model configured toreceive input having two modalities, the process 300 may be modified totrain a multi-modal statistical model configured to receive input frommore than two modalities (e.g., three, four, five, six, seven, eight,nine, ten, etc. modalities. In some such embodiments, the joint modalityrepresentation and a modality embedding for each of the multiplemodalities would be learned during the self-supervised learning stage(act 306). The predictor and a task embedding for each of the multiplemodalities would be learned during the supervised learning stage (act308).

As described above, in some embodiments, the encoder and decoder foreach of the modalities may be learned prior to the execution of process300. In some embodiments, however, one or more of the encoder(s) and/ordecoder(s) may be learned during process 300 such that their parametervalues are estimated for the first time and/or updated during process300.

Additional aspects of the techniques for training a multi-modalstatistical model may be appreciated from the following discussion ofthe self-supervised and supervised training stages.

Self-Supervised Training Phase

Let x_(i)∈X_(i) be an input data point for the modality i, and lett_(i)∈T_(i) be the compressed representation of x_(i) such that:t _(i)=ψ_(i)(x _(i)),

where ψ_(i) is the encoding function representing the encoder for theith modality. Let the joint modality representation (sometimes referredto as a knowledge base herein) be an n×m matrix M, where n denotes thenumber of entries in the joint modality representation and m denotes thedimensionality of each entry.) The joint modality representation may belinearly projected to the representation space of the ith modality byusing the modality embedding E_(i) (an m×d_(i) matrix, which is learnedduring the self-supervised training phase):{tilde over (M)} _(i) =ME _(t).

Then the cosine similarity between the representation t_(i) and the rowsof the projected joint modality representation {tilde over (M)}_(i)gives us similarity scores over each entry of the joint modalityrepresentation (e.g., each row of the memory matrix), which may then beconverted to probability using a softmax function, approximating p (m|t)according to:

${s_{i} = {{\overset{\sim}{M}}_{i}t_{i}}}{{p\left( m_{k} \middle| t_{i} \right)} = \frac{e^{s_{{ik}/}\tau}}{\Sigma_{k}e^{s_{{ik}/^{\tau}}}}}$

where τ is the temperature variable, accounting for thesharpness/entropy of the distribution. The weighted average of theprojected joint modality representation matrix entries {tilde over(t)}_(i) is then provided as input to the ith modality decoder Φ_(i):

${{\overset{˜}{t}}_{i} = {\sum\limits_{k}{{p\left( m_{k} \middle| t_{i} \right)}m_{k}}}}{{\overset{\hat{}}{x}}_{i} = {\Phi_{i}\left( {\overset{˜}{t}}_{i} \right)}}$

The gradient of the reconstruction loss with respect to at least some ofthe network parameters (e.g., some or all of the parameter values of theencoder, decoder, joint modality representation, and the modalityembedding) is back propagated and the parameters are updated viastochastic gradient descent algorithm:θ_(j,t+1)=θ_(j,t) +λV _(θ) _(j,t)

({circumflex over (x)} _(i) x _(i))+μ_(t)where θ_(j,t) is the j^(th) parameter at time t; λ and μ are thelearning rate and momentum parameters, respectively, and

( ) is the loss function. The loss function may be cross-entropy,Kullback-Liebler divergence, L1 distance, L2 distance (Euclideandistance), and/or any other suitable loss function, as aspects of thetechnology described herein are not limited in this respect.

Supervised Training Stage

We define task as predicting labels or values denoted by y∈Y. In thepresence of data pairs (X_(i), Y_(j)), we use the joint modalityrepresentation trained during the self-supervised learning stage andencoder ψ_(i)(x_(i)) for x_(i)∈X_(i) to generate the representationt_(i)∈T_(i) as shown in the equations above. Then a Hadamard product isperformed between the feature representation {tilde over (t)}_(i) andthe task embeddings U_(j) according to:ũ _(ij) =u _(j) ⊙{tilde over (t)} _(i)

Finally for the forward pass, we provide the projected representation tothe task predictorΠ_(j) {tilde over (y)} _(j)=Π_(j)(ũ _(ij))

An appropriate loss function is chosen for task type. For example, ifthe task is a multi-label exclusive classification, cross-entropy lossmay be used. As another example, if the task is a prediction of acontinuous distribution, an information-theoretic measure such asKullback-Leibler divergence may be used as the loss function. Regardlessof the choice of the loss function, the gradients of the loss withrespect to the parameters of task predictor Π_(j) and task embeddingU_(j) may be calculated and back-propagated, as described in thestochastic gradient descent equation shown above.

Using Multi-Modal Statistical Models for Prediction

FIG. 4 is a flowchart of an illustrative process 400 for using amulti-modal statistical model for a prediction task, in accordance withsome embodiments of the technology described herein. The process 400 maybe performed by any suitable computing device(s). For example, theprocess 400 may be performed by one or more graphics processing units(GPUs), one or more computing device(s) provided by a cloud computingservice, and/or any other suitable computing device(s), as aspects ofthe technology described herein are not limited in this respect.

In this example, it is assumed that prior to the start of the process400, a multi-modal statistical model configured to receive input for atleast two different modalities has been trained and its parameters havebeen stored. For example, prior to the start of process 400, amulti-modal statistical model may have been trained using the two-stagetraining process 300, which is described herein.

Process 400 begins at act 402, where information specifying apreviously-trained multi-modal statistical model is accessed. Theinformation specifying the multi-modal statistical model may be in anysuitable format and may be accessed from local storage, over a networkfrom remote storage, or any other suitable source(s), as aspects of thetechnology described herein are not limited in this respect. Theinformation may include values for parameters of the multi-modalstatistical model. The multi-modal statistical model may includecomponents having parameters and the information specifying the modelmay include parameter values for parameters for each of one or more ofthese components. For example, a multi-modal statistical model mayinclude a joint modality representation, a predictor and, for each ofmultiple modalities, a respective encoder, a respective modalityembedding, and a respective task embedding, and the information accessedat act 402 may include values for these components.

In the embodiment described with reference to FIG. 4 , it is assumedthat the multi-modal statistical model (for which parameter areaccessed) is configured to receive input from two modalities—a firstmodality and a second modality. However, it should be appreciated that,in other embodiments, the multi-modal statistical model may beconfigured to receive input from any suitable number of modalities(e.g., three, four, five, six, seven, eight, nine, ten, eleven, twelve,etc.), as aspects of the technology described herein are not limited inthis respect.

Next, process 400 proceeds to act 404, where input data is obtained forthe first data modality (e.g., protein sequence data). In someembodiments, the input data may be converted or otherwise pre-processedinto a representation suitable for providing to the encoder for thefirst modality. For example, categorical data may be one-hot encodedprior to being provided to the encoder for the first modality. Asanother example, image data may be resized prior to being provided tothe encoder for the first modality. In other embodiments, however, noconversion and/or pre-processing may be required or performed.

Next, process 400 proceeds to act 406, where the input data is providedas input to the first encoder, which generates a first feature vector asoutput. For example, as shown with reference to FIG. 2B, input 202 formodality “A”, is provided as input to the encoder 204 for modality “A”,and the encoder 204 produces a first feature vector (e.g., featurerepresentation 206 as output).

Next, process 400 proceeds to act 408, where the first feature vectorgenerated at act 406 (at the output of the first encoder) is used,together with the joint modality representation and the first modalityembedding to generate a second feature vector. For example, as shownwith reference to FIG. 2B, the first feature vector (e.g., featurerepresentation 206) may be used together with one of the modalityembeddings 232 and the knowledge base 230 to identify (e.g., generate orselect) the second feature vector (e.g., feature representation 208).

The second feature vector may be identified in any of the ways describedherein. For example, in some embodiments, identifying the second featurevector may include: (1) projecting the joint modality representation(e.g., knowledge base 230) to the space of the first modality to obtaina plurality of projected vectors; (2) calculating a distance (e.g., acosine distance and/or any other suitable type of distance measure)between each of the plurality of projected vectors and the first featurevector (e.g., feature representation 206), and using these distances tocalculate weights for the projected vectors (e.g., by using a soft-maxweighting); and (3) generating the second feature vector as a weightedsum of the projected vectors weighted by the calculated weights. Forexample, the joint modality representation may include N m-dimensionalvectors (which may be represented and/or stored as an N×m matrix), andprojecting the joint modality representation using a first modalityprojection, which may be represented as an m×d to the first modality mayproduce N d-dimensional vectors (which may be represented an as an N×dmatrix). The distance between the first feature vector output by thefirst encoder (e.g., feature representation 206 shown in FIG. 2A) andeach of the N d-dimensional vectors may be calculated and used to obtainweights for each of the N d-dimensional vectors. Then the second featurevector (e.g., feature representation 208) may be calculated as aweighted sum of the N d-dimensional vectors, with the vectors beingweighted by the calculated weights. In other embodiments, the secondfeature vector may be identified by selecting, from among the Nd-dimensional projected vectors, the vector closest to the first featurevector generated by the first encoder according to a suitably-chosendistance measure (e.g., cosine distance), rather than a weighted averageof multiple d-dimensional vectors in the projected joint modalityrepresentation.

Next, process 400 proceeds to act 410, where the second feature vectoris used to generate a prediction for a prediction task using thepredictor and a task embedding for the first modality (both of which arecomponents in the multi-modal statistical model). This may be done inany suitable way. For example, the task embedding for the first modalitymay have a dimensionality that is the same as that of the second featurevector. In this example, the weights of the task embedding may be usedto point-wise multiply the values of the second feature vector (e.g., inthe sense of a Hadamard product) to generate input to the predictor. Inturn, the predictor may output the prediction for the task based on thisinput. For example, as shown in FIG. 2B, the second feature vector(e.g., representation 208) may be point-wise modified (e.g., multiplied)by the first task embedding of task embeddings 254 and provided as inputto predictor 252 to produce an output for prediction task 256.

As may be appreciated from the above description of process 400, themulti-modal statistical model may be used to generate a prediction for atask using input only from a single modality. This means that wheninputs are available from multiple different modalities at differenttimes, they may be provided as inputs to the multi-modal statisticalmodel when they become available—asynchronously.

In some embodiments, the multi-modal statistical model may be operatedsynchronously and may be used to process paired inputs from twomodalities or linked inputs from more than two modalities. For example,a first input for the first modality (e.g., input 202) may be providedas input to the encoder for the first modality (e.g., encoder 204) togenerate a first feature vector (e.g., feature representation 206), andthe first feature vector may be used, together with the joint modalityrepresentation (e.g., knowledge base 230) and first modalityrepresentation (e.g., of modality representations 232) to identify(e.g., generate or select) a second feature vector (e.g., featurerepresentation 208). In this example, the first input for the firstmodality (e.g., input 202) may be paired (e.g., provided at the sametime as input to the multi-modal statistical model) with first input forthe second modality (e.g., input 212). The first input for the secondmodality (e.g., input 212) may be provided as input to the encoder forthe second modality (e.g., encoder 214) to identify (e.g., generate orselect) a third feature vector (e.g., feature representation 216), andthe first feature vector may be used, together with the joint modalityrepresentation (e.g., knowledge base 230) and second modalityrepresentation (e.g., of modality representations 232) to generate afourth feature vector (e.g., feature representation 218). In turn, thesecond and fourth feature vectors may be modified by the task embeddingsfor the first and second modalities, and the result may be combined(e.g., by a coordinate-wise addition 260) and be provided as inputs tothe predictor (e.g., predictor 252) to provide a prediction for task256.

Example: Protein Structure Prediction

In this section, the techniques for unifying deep learning statisticalmodels for different data modalities described herein are illustratedfor an example problem of predicting protein structure. Conventionaltechniques to building predictive models in molecular biology often fallshort, with the resulting models lacking desired performancecharacteristics (e.g., precision).

Building a common framework to accommodate predictive modeling ofvarious types of biological data available is highly challenging for avariety of reasons, including:

-   -   Source Heterogeneity: There are potentially thousands of        different molecular entities that may be probed and the data we        acquire come in various forms or modalities.    -   High Dimensionality: Observed data sparsely samples the all        possible configurations of the input space. Therefore, most of        the time the available data are sparse and insufficient.    -   Experimental Noise: Biological data acquisition is often noisy        and suffers from experimental biases and idiosyncrasies    -   Unmatched Modalities and Incompleteness: Experiments and        observations are limited to only a couple of modalities at a        time, which results in highly incomplete data.

Conventional approaches to building high-quality predictive models insuch a challenging modeling context rely on strong priors, which expressdeep domain-level expertise and knowledge. However, our ability tospecify such priors is limited by the amount of domain-level knowledgeavailable. For example, without an extensive domain knowledge,functionally annotating a protein sequence of a newly discovered speciescan be done by performing a BLAST query (finding the closest knownsequences) and transferring the functional assignments from the tophits. However, this approach is reported to be very poor and misleadingespecially when identifying which biological process the protein ofinterest is involved in. Better performing models require years ofaccumulated domain knowledge about proteins, amino acid motifs, theirparticipations in biological processes, and the like.

The techniques described herein address the above-described challengesby accommodating multiple modalities without requiring training data tocontain fully matching data points (with each data point including acontribution from each of multiple different modalities). The jointmodality representation described herein provides a data-driven priorfor cross-modality feature extraction, which regularizes the individualmodels and alleviates extra compression. Every bit of extra compressionis equivalent to having twice as much labeled data.

The techniques described herein are illustrated below on a proteinfunction prediction task. First, we downloaded the Swiss-Prot database,which contains 554,452 proteins, and selected six different datamodalities including: (1) protein sequence; (2) pfam domains; (3)biological process ontology; (4) molecular function ontology; (5)cellular component ontology; and (6) the taxonomic family of thespecies. The functional annotations (ontologies) are highly incompleteand possibly noisy. Proteins which are defined as a test set for thesecond Critical Assessment of Functional Annotation (CAFA2) consortiumwere excluded to facilitate evaluation of the results.

Implementation Details

Although functional ontology prediction is our task, we treated theseontologies as individual modalities. In order to apply the techniquesdescribed herein to the functional ontology prediction task, we need tospecify aspects of the encoders, decoders, the joint modalityrepresentation, the modality embeddings, and the task embeddings.

Encoders

In this illustrative example, the encoder for protein sequence inputsincludes four convolutional blocks each of which contains a 1Dconvolution with 10 filters of size 20, followed by a layernormalization, one-dimensional max-pooling of size 3 with stride 3, anda rectified linear unit (ReLU) activation. After the four convolutionalblocks, the encoder includes another convolutional layer with 10 kernelsof size 11 and an adaptive 1 d max-pooling to size 1. As a result, theprotein sequence encoder takes 10×1024 one-hot-encoded protein sequenceinput (if the sequence is shorter than 1024, the input is padded withall zeros) and returns 10×1 latent representation.

We used embedding dictionaries as encoders of categorical data sources.Indexing an embedding dictionary is equivalent to forwarding aone-hot-encoded input data to a linear layer without a bias term, butcomputationally much more efficient as the input is highly sparse. Thesizes of the embedding dictionaries are one more than the number ofcategories in each modality as the first entry is always reserved for anunknown category or padding index. The actual sizes we used in theexperiment are 24937, 9572, 3185, 1779, and 11679 for biologicalprocess, molecular function, cellular component, taxonomic family, andpfam domains, respectively. The dimension of the embeddings is chosen tobe 10.

Decoders

The protein sequence decoder comprises six consecutive layers ofdeconvolution blocks. Each block contains a deconvolution operationwhere the number of filters are 128, the filter size is 6, stride is 3and both ends are padded with 1, followed by a layer normalization andleaky ReLU activation of slope 0.1.

The decoders of categorical modalities are chosen to be a fullyconnected linear layers of size 10×N, which takes the representationreturned from the joint modality representation (e.g., knowledge base)and returns sigmoid-activated scores over all classes (N is the numberof classes in each modalities).

Joint Modality Representation and Modality Projections

The joint modality representation comprises 512 vectors of dimension 64.In this example, these vectors may be stored in a matrix of size 512×64.The rows are L2 normalized after each update. Since there are sixmodalities in this example, there are six modality embeddings, each ofwhich is represented using a matrix of size 64×10. Each modalityembedding projects the joint modality representation into therepresentation space of the respective modality.

Loss Functions

For sequence reconstruction, we used cross entropy loss calculated for aprobability distribution over 20 possible amino acids for every aminoacid residue in the sequence. We excluded the padded regions. For 3ontology modalities and the pfam domain modality, we used max-marginloss with a negative sampling procedure and margin value 1. For thetaxonomic family modalities, we used cross entropy.

Training

We used a variant of SGD optimizer called “Adam” with a learning rate of10⁻³, and a batch size of 25. We tested both two different scenarios:(1) Synchronous training with paired data; and (2) Asynchronous trainingwith unpaired data.

When training with paired data, the joint modality representationweights are updated with respect to the sum of the gradients contributedfrom all reconstruction losses, across all modalities, similar to allother parameters.

When training asynchronously, the parameters for each of the modalitiesare trained one by one by querying the joint modality representation.The joint modality representation weights are updated every time amodality is trained with its own reconstruction objective. We went overall modalities 3 times and each time trained until their fullconvergence. We reduced the learning rate on the joint modalityrepresentation parameters every time a modality is trained.

Results

As shown in FIG. 5 , the early experiments demonstrate that multi-modalstatistical model described above for the functional annotation ofproteins performs significantly better than competing conventionalapproaches other models, all of which requires extensive featureengineering. As shown in FIG. 5 , the average AUROC (area under receiveroperating characteristic curve) for the multi-modal statistical modeldescribed above is higher than that of competing conventionalapproaches. The performance of the competing approaches shown in FIG. 5is discussed further in an article titled “An expanded evaluation ofprotein function prediction methods shows an improvement in accuracy,”published on Sep. 7, 2016 in Genome Biology, volume 17, page 184, whicharticle is incorporated by reference herein in its entirety.

Theoretical Underpinnings

Further aspects of the multi-modal statistical models described hereinmay be appreciated from the following discussion.

Extracting Relevant Information

Let X denote the signal (message) space with a fixed probability measureρ(x), and the T denote its quantized codebook or compressedrepresentation.

For each x∈X we seek a possibly stochastic mapping to a representativeor codeword in a codebook, t∈T characterized by a conditionalprobability density function (pdf) p(t|x). This mapping induces a softpartitioning of X in which each block is associated with the codebookelements t∈T with probability p(t|x). The total probability of thecodeword t∈T is given by:p(t)=Σ_(x) p(t|x)p(x).

The average volume of the elements of X that are mapped to the samecodeword is 2^(H(X|T)) where

${H\left( X \middle| T \right)} = {{\sum\limits_{t}{{p(t)}{H\left( {\left. X \middle| T \right. = t} \right)}}} = {- {\sum\limits_{t}{{p(t)}{\sum\limits_{x}{{p\left( x \middle| t \right)}\log\left( {p\left( x \middle| t \right)} \right)}}}}}}$

The quality of quantization is determined by the “rate” or “average bitsper message” needed to specify an element in the codebook withoutconfusion. This number per element of X is bounded from below by themutual information

${I\left( {X;T} \right)} = {\sum\limits_{x \in X}{\sum\limits_{t \in T}{{p\left( {x,t} \right)}\log\left( \frac{p\left( x \middle| t \right)}{p(t)} \right)}}}$

This equation may be thought as the average cardinality of thepartitioning of X which is given by the ratio of volume of X to that ofthe mean partition, i.e.

$K = {\frac{2^{H(X)}}{2^{H({X|T})}} = 2^{I({X;T})}}$

Information Bottleneck

Ultimately, for any predictive task, we would like to learn a mapping p(t|x) from an input space X to a representation space T which onlyretain the relevant information for the prediction (label) space Y. Inother words, we would like to minimize the mutual information between Xand T while maximizing the mutual information between T and Y which canbe captured by minimizing the following functional with respect to themapping p(t|x):L[p(t|x)]=I(X;T)−βI(Y;T)where β is the tradeoff parameter.

Input Compression Bound

For the best prediction performance, our objective is to maximize I (T;Y) which is restricted to the upper bound I(T; Y)≤I(X; Y) due to thedata processing inequality. If we had unlimited amount of data in X andY, we could approximate the joint distribution p(x, y) arbitrarily welland therefore, we would not need a compact representation of X. However,because the amount of data is often limited, p(x|y) cannot be estimatedsufficiently well. Therefore, we have to regularize the model bycompressing the input—reducing the complexity by minimizing I(X; T).

Let Î denote the empirical estimate of the mutual information from thelimited samples. The generalization bound has been shown to be:

${{I\left( {T;Y} \right)} \leq {{\overset{\hat{}}{I}\left( {T;Y} \right)} + {O\left( \frac{{❘T❘}{❘Y❘}}{\sqrt{n}} \right)}}}{and}{{I\left( {T;X} \right)} \leq {{\overset{\hat{}}{I}\left( {T;X} \right)} + {O\left( \frac{❘T❘}{\sqrt{n}} \right)}}}$

Notably, the upper bound depends on the cardinality of therepresentation K=|T|2^(I(T;X)). In other words, an additional single bitof extra compression is equivalent to doubling the size of data for thesame generalization gap.

Compression for Multi-Modal Prediction

Consider a simple cross-modality prediction setting, where modalities X₁and X₂ are compressed into T₁ and T₂ representations, which are supposedto predict X₂ and X₁, respectively. As shown in FIG. 6A, the observedvariables X₁ and X₂ are represented by latent random variables T₁ andT₂, which are compressed representations of X₁ and X₂. The latent randomvariables T₁ and T₂ for first and second modalities may be defined asthe outputs of encoders for the first and second modalities,respectively. As shown in FIG. 6B, the latent random variables T₁ and T₂may be used to predict the variables X₁ and X₂. The decoders for thefirst and second modalities, respectively, may be used to predict thevariables X₁ and X₂ from the latent representations T₁ and T₂

In this situation, the Lagrangian to minimize is given by:L=I(T ₁ ;X ₁)+I(T ₂ ;X ₂)−γI(T ₁ ;T ₂)

Therefore, while we are compressing, we also want to make sure that thecompressed representations T₁ and T₂ are as informative about one otheras possible. This equation indicates that we should maximally compressX₁ and X₂ by minimizing the mutual information between X₁, T₁ and X₂,T₂, while maximizing the mutual information (correlation) between T₁ andT₂. In the framework described herein, maximizing the mutual informationbetween T₁ and T₂ may be achieved by forcing each encoded input to bematched to a single or a weighted average of code-words in acodebook—the joint modality representation (e.g., knowledge base 230);the matched entry is then provided as input to the decoder during theself-supervised training stage.

Intuitively, by learning a cross-modality driven compressedrepresentations, we are leveraging the labeled (or paired) data acrossmany modalities, which reduces the generalization gap.

An illustrative implementation of a computer system 700 that may be usedin connection with any of the embodiments of the disclosure providedherein is shown in FIG. 7 . The computer system 700 may include one ormore computer hardware processors 700 and one or more articles ofmanufacture that comprise non-transitory computer-readable storage media(e.g., memory 720 and one or more non-volatile storage devices 730). Theprocessor(s) 710 may control writing data to and reading data from thememory 720 and the non-volatile storage device(s) 730 in any suitablemanner. To perform any of the functionality described herein, theprocessor(s) 710 may execute one or more processor-executableinstructions stored in one or more non-transitory computer-readablestorage media (e.g., the memory 720), which may serve as non-transitorycomputer-readable storage media storing processor-executableinstructions for execution by the processor(s) 710.

The terms “program” or “software” are used herein in a generic sense torefer to any type of computer code or set of processor-executableinstructions that can be employed to program a computer or otherprocessor (physical or virtual) to implement various aspects ofembodiments as discussed above. Additionally, according to one aspect,one or more computer programs that when executed perform methods of thedisclosure provided herein need not reside on a single computer orprocessor, but may be distributed in a modular fashion among differentcomputers or processors to implement various aspects of the disclosureprovided herein.

Processor-executable instructions may be in many forms, such as programmodules, executed by one or more computers or other devices. Generally,program modules include routines, programs, objects, components, datastructures, etc. that perform particular tasks or implement particularabstract data types. Typically, the functionality of the program modulesmay be combined or distributed.

Also, data structures may be stored in one or more non-transitorycomputer-readable storage media in any suitable form. For simplicity ofillustration, data structures may be shown to have fields that arerelated through location in the data structure. Such relationships maylikewise be achieved by assigning storage for the fields with locationsin a non-transitory computer-readable medium that convey relationshipbetween the fields. However, any suitable mechanism may be used toestablish relationships among information in fields of a data structure,including through the use of pointers, tags or other mechanisms thatestablish relationships among data elements.

Various inventive concepts may be embodied as one or more processes, ofwhich examples have been provided. The acts performed as part of eachprocess may be ordered in any suitable way. Thus, embodiments may beconstructed in which acts are performed in an order different thanillustrated, which may include performing some acts simultaneously, eventhough shown as sequential acts in illustrative embodiments.

As used herein in the specification and in the claims, the phrase “atleast one,” in reference to a list of one or more elements, should beunderstood to mean at least one element selected from any one or more ofthe elements in the list of elements, but not necessarily including atleast one of each and every element specifically listed within the listof elements and not excluding any combinations of elements in the listof elements. This definition also allows that elements may optionally bepresent other than the elements specifically identified within the listof elements to which the phrase “at least one” refers, whether relatedor unrelated to those elements specifically identified. Thus, forexample, “at least one of A and B” (or, equivalently, “at least one of Aor B,” or, equivalently “at least one of A and/or B”) can refer, in oneembodiment, to at least one, optionally including more than one, A, withno B present (and optionally including elements other than B); inanother embodiment, to at least one, optionally including more than one,B, with no A present (and optionally including elements other than A);in yet another embodiment, to at least one, optionally including morethan one, A, and at least one, optionally including more than one, B(and optionally including other elements); etc.

The phrase “and/or,” as used herein in the specification and in theclaims, should be understood to mean “either or both” of the elements soconjoined, i.e., elements that are conjunctively present in some casesand disjunctively present in other cases. Multiple elements listed with“and/or” should be construed in the same fashion, i.e., “one or more” ofthe elements so conjoined. Other elements may optionally be presentother than the elements specifically identified by the “and/or” clause,whether related or unrelated to those elements specifically identified.Thus, as a non-limiting example, a reference to “A and/or B”, when usedin conjunction with open-ended language such as “comprising” can refer,in one embodiment, to A only (optionally including elements other thanB); in another embodiment, to B only (optionally including elementsother than A); in yet another embodiment, to both A and B (optionallyincluding other elements); etc.

Use of ordinal terms such as “first,” “second,” “third,” etc., in theclaims to modify a claim element does not by itself connote anypriority, precedence, or order of one claim element over another or thetemporal order in which acts of a method are performed. Such terms areused merely as labels to distinguish one claim element having a certainname from another element having a same name (but for use of the ordinalterm). The phraseology and terminology used herein is for the purpose ofdescription and should not be regarded as limiting. The use of“including,” “comprising,” “having,” “containing”, “involving”, andvariations thereof, is meant to encompass the items listed thereafterand additional items.

Having described several embodiments of the techniques described hereinin detail, various modifications, and improvements will readily occur tothose skilled in the art. Such modifications and improvements areintended to be within the spirit and scope of the disclosure.Accordingly, the foregoing description is by way of example only, and isnot intended as limiting. The techniques are limited only as defined bythe following claims and the equivalents thereto.

What is claimed is:
 1. A system for generating a prediction for aprediction task using a multi-modal statistical model configured toreceive input data from multiple modalities including input data from afirst modality and input data from a second modality different from thefirst modality, the system comprising: at least one computer hardwareprocessor; and at least one non-transitory computer-readable storagemedium storing instructions that, when executed by the at least onecomputer hardware processor, cause the at least one computer hardwareprocessor to perform: obtaining information specifying the multi-modalstatistical model including values of parameters of multiple componentsof the multi-modal statistical model, the multiple components includingfirst and second encoders for processing input data for the first andsecond modalities, first and second modality embeddings, ajoint-modality representation, and a predictor, wherein: the first andsecond modality embeddings comprise a plurality of weights and vectorsfor projecting the joint-modality representation into respective firstand second modality spaces; obtaining first input data for the firstdata modality; providing the first input data to the first encoder togenerate a first feature vector; identifying a second feature vectorusing the joint-modality representation, the first modality embeddingand the first feature vector; and generating the prediction for theprediction task using the predictor and the second feature vector. 2.The system of claim 1, wherein identifying the second feature vectorusing the joint-modality representation, the first modality embedding,and the first feature vector comprises: projecting, using the firstmodality embedding, the joint-modality representation into the firstmodality space to obtain a first projection of the joint-modalityrepresentation; and identifying the second feature using the firstprojection of the joint-modality representation.
 3. The system of claim2, wherein, the first projection of the joint-modality representationcomprises a plurality of projected vectors; and identifying the secondfeature using the first projection of the joint-modality representationcomprises: calculating a distance between each of the plurality ofprojected vectors and the first feature vector; and generating thesecond feature vector using the plurality projected vectors anddistances from the first feature vector.
 4. The system of claim 3,wherein generating the second feature using the plurality projectedvectors and the distances from the first feature vector comprises: usingthe distances between the plurality of projected vectors and the firstfeature vector to calculate weights for the projected vectors; andgenerating the second feature vector using the plurality of projectedvectors and the weights.
 5. The system of claim 3, wherein generatingthe second feature using the plurality projected vectors and thedistances comprises: selecting, from the plurality of projected vectors,a projected vector that is closest to the first feature vector as thesecond feature vector.
 6. The system of claim 1, wherein theinstructions further cause the at least one computer hardware processorto perform: obtaining second input data for the second data modality;providing the second input data to the second encoder to generate athird feature vector; identifying a fourth feature vector using thejoint-modality representation, the second modality embedding and thethird feature vector; wherein generating the prediction for theprediction task comprises generating the prediction using the fourthfeature vector.
 7. The system of claim 6, wherein generating theprediction for the prediction task comprises: generating input to thepredictor using the second feature vector and the fourth feature vector;and providing the input to the predictor to obtain the prediction forthe prediction task.
 8. The system of claim 7, wherein, the multiplecomponents of the multi-modal statistical model comprise a first taskembedding for the first modality and a second task embedding for thesecond modality; and generating the input to the predictor using thesecond feature vector and the fourth feature vector comprises: weightingthe second feature vector using the first task embedding to obtain aweighted second feature vector; weighting the fourth feature vectorusing the second task embedding to obtain a weighted fourth featurevector; and generating the input to the predictor using the weightedsecond and fourth feature vectors.
 9. The system of claim 6, wherein theprediction task comprises a prediction of function of a protein.
 10. Thesystem of claim 9, wherein the input data for the first modalitycomprises protein sequence data.
 11. The system of claim 10, wherein theprotein sequence data comprises a one-hot-encoded protein sequence. 12.The system of claim 10, wherein the input data for the second modalitycomprises protein family data, biological process ontology data,molecular function ontology data, cellular component ontology data, ortaxonomic species family data.
 13. A method for generating a predictionfor a prediction task using a multi-modal statistical model configuredto receive input data from multiple modalities including input data froma first modality and input data from a second modality different fromthe first modality, the method comprising: using at least one computerhardware processor to perform: obtaining information specifying themulti-modal statistical model including values of parameters of multiplecomponents of the multi-modal statistical model, the multiple componentsincluding first and second encoders for processing input data for thefirst and second modalities, first and second modality embeddings, ajoint-modality representation, and a predictor, wherein: the first andsecond modality embeddings comprise a plurality of weights and vectorsfor projecting the joint-modality representation into respective firstand second modality spaces; obtaining first input data for the firstdata modality; providing the first input data to the first encoder togenerate a first feature vector; identifying a second feature vectorusing the joint-modality representation, the first modality embeddingand the first feature vector; and generating the prediction for theprediction task using the predictor and the second feature vector. 14.The method of claim 13, wherein identifying the second feature vectorusing the joint-modality representation, the first modality embedding,and the first feature vector comprises: projecting, using the firstmodality embedding, the joint-modality representation into the firstmodality space to obtain a first projection of the joint-modalityrepresentation; and identifying the second feature using the firstprojection of the joint-modality representation.
 15. The method of claim14, wherein, the first projection of the joint-modality representationcomprises a plurality of projected vectors; and identifying the secondfeature using the first projection of the joint-modality representationcomprises: calculating a distance between each of the plurality ofprojected vectors and the first feature vector; and generating thesecond feature vector using the plurality projected vectors anddistances from the first feature vector.
 16. The method of claim 13,further comprising: obtaining second input data for the second datamodality; providing the second input data to the second encoder togenerate a third feature vector; and identifying a fourth feature vectorusing the joint-modality representation, the second modality embeddingand the third feature vector; wherein generating the prediction for theprediction task comprises generating the prediction using the fourthfeature vector.
 17. The method of claim 16, wherein the prediction taskcomprises a prediction of function of a protein.
 18. The method of claim17, wherein the input data for the first modality comprises proteinsequence data.
 19. The method of claim 18, wherein the input data forthe second modality comprises protein family data, biological processontology data, molecular function ontology data, cellular componentontology data, or taxonomic species family data.
 20. At least onenon-transitory computer-readable storage medium storing instructionsthat, when executed by at least one computer hardware processor, causethe at least one computer hardware processor to perform a method forgenerating a prediction for a prediction task using a multi-modalstatistical model configured to receive input data from multiplemodalities including input data from a first modality and input datafrom a second modality different from the first modality, the methodcomprising: obtaining information specifying the multi-modal statisticalmodel including values of parameters of multiple components of themulti-modal statistical model, the multiple components including firstand second encoders for processing input data for the first and secondmodalities, first and second modality embeddings, a joint-modalityrepresentation, and a predictor, wherein: the first and second modalityembeddings comprise a plurality of weights and vectors for projectingthe joint-modality representation into respective first and secondmodality spaces; obtaining first input data for the first data modality;providing the first input data to the first encoder to generate a firstfeature vector; identifying a second feature vector using thejoint-modality representation, the first modality embedding and thefirst feature vector; and generating the prediction for the predictiontask using the predictor and the second feature vector.